import { CellComplex, VecN, type CellGroup, type SourceCellIdN, type SourceCellReferenceN } from '@holotope/core';
import type { SimplexConstitutiveEvaluationN } from './simplex-constitutive.js';
import type { SimplexConstitutiveHessianVectorEvaluationN } from './simplex-constitutive-curvature.js';
import type { XpbdConservativeHessianBlockN, XpbdConservativeHessianVectorEvaluationN, XpbdParticleDirectionQueryN } from './xpbd-incremental-potential-analytic-curvature.js';
import { XpbdParticleN, XpbdWorldN, type XpbdConservativeForceProviderN, type XpbdForceProviderEvaluationN, type XpbdParticlePositionQueryN } from './xpbd-world.js';
/** Pure dimension-independent constitutive evaluator used by family assembly. */
export interface SimplexConstitutiveLawN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> {
    readonly id: string;
    evaluate(restPositions: readonly VecN[], currentPositions: readonly VecN[], material: TMaterial): TEvaluation;
    /**
     * Optional exact matrix-free curvature capability for this law.
     *
     * Its products use the mathematical potential sign
     * `Hessian(U) * direction`.
     */
    evaluateHessianVector?(restPositions: readonly VecN[], currentPositions: readonly VecN[], directions: readonly VecN[], material: TMaterial): SimplexConstitutiveHessianVectorEvaluationN<TEvaluation>;
}
/** Source-side identity of one compiled element, before any material is chosen. */
export interface SimplexConstitutiveFamilyElementContextN {
    /** Ordinal of the source cell this element was compiled from. */
    readonly sourceCellIndex: number;
    /** Source vertex ordinals of the element, in the cell's own order. */
    readonly sourceVertexIndices: readonly number[];
    /** Structural source-cell identity, stable across regeneration. */
    readonly sourceId: SourceCellIdN;
    /** Intrinsic simplex dimension `k`, one less than its vertex count. */
    readonly simplexDimension: number;
    /** Undeformed k-measure, the reference the energy density is scaled by. */
    readonly restMeasure: number;
}
export type SimplexConstitutiveFamilyMaterialN<TMaterial> = TMaterial | ((element: SimplexConstitutiveFamilyElementContextN) => TMaterial);
export interface CompileSimplexConstitutiveFamilyNOptions<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> {
    readonly id: string;
    readonly source: CellComplex;
    readonly simplexGroup: CellGroup;
    /** One live particle per source vertex, in source-vertex order. */
    readonly particles: readonly XpbdParticleN[];
    readonly law: SimplexConstitutiveLawN<TMaterial, TEvaluation>;
    readonly material: SimplexConstitutiveFamilyMaterialN<TMaterial>;
}
/** One compiled element: its source identity together with its material. */
export interface SimplexConstitutiveFamilyElementN<TMaterial> extends SimplexConstitutiveFamilyElementContextN {
    /** Provenance record tying this element back to the cell it came from. */
    readonly sourceReference: SourceCellReferenceN;
    /** Material resolved for this element, uniform or per-element. */
    readonly material: TMaterial;
}
/** One element paired with what its law reported at the current state. */
export interface SimplexConstitutiveFamilyElementEvaluationN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> {
    /** The compiled element the evaluation belongs to. */
    readonly element: SimplexConstitutiveFamilyElementN<TMaterial>;
    /** Complete law evaluation at this element's current positions. */
    readonly evaluation: TEvaluation;
}
export interface SimplexConstitutiveFamilyEvaluationN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> extends XpbdForceProviderEvaluationN {
    readonly lawId: string;
    readonly potentialEnergy: number;
    /** One entry per source simplex, in source-cell order. */
    readonly elements: readonly SimplexConstitutiveFamilyElementEvaluationN<TMaterial, TEvaluation>[];
    readonly maximumStrainFrobeniusNorm: number;
    readonly minimumMeasureRatio: number;
    readonly invertedElementCount: number;
    readonly collapsedElementCount: number;
    /** Norm of the summed internal forces. */
    readonly netForceResidual: number;
}
/** One simplex's exact contribution to a family Hessian-vector product. */
export interface SimplexConstitutiveFamilyElementHessianVectorEvaluationN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> {
    /** Source-identified simplex whose local product was evaluated. */
    readonly element: SimplexConstitutiveFamilyElementN<TMaterial>;
    /** Exact law-level directional tensors and vertex products for the simplex. */
    readonly evaluation: SimplexConstitutiveHessianVectorEvaluationN<TEvaluation>;
}
/** One source-simplex block in an exact constitutive Hessian decomposition. */
export interface SimplexConstitutiveFamilyHessianBlockN<TMaterial> extends XpbdConservativeHessianBlockN {
    /** Compiled source element whose law contributes this block. */
    readonly element: SimplexConstitutiveFamilyElementN<TMaterial>;
}
/** Exact assembled potential curvature for one constitutive family. */
export interface SimplexConstitutiveFamilyHessianVectorEvaluationN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> extends XpbdConservativeHessianVectorEvaluationN {
    /** Stable constitutive-law identity shared with first-order evaluation. */
    readonly lawId: string;
    /** One exact contribution per source simplex, in source-cell order. */
    readonly elements: readonly SimplexConstitutiveFamilyElementHessianVectorEvaluationN<TMaterial, TEvaluation>[];
    /** Norm of the summed products; internal translation invariance makes it zero. */
    readonly netProductResidual: number;
}
/** Source-identified constitutive elements assembled over shared RN particles. */
export declare class SimplexConstitutiveFamilyN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>> implements XpbdConservativeForceProviderN {
    readonly id: string;
    readonly dimension: number;
    readonly source: CellComplex;
    readonly sourceSimplexGroup: CellGroup;
    readonly particles: readonly XpbdParticleN[];
    readonly law: SimplexConstitutiveLawN<TMaterial, TEvaluation>;
    readonly elements: readonly SimplexConstitutiveFamilyElementN<TMaterial>[];
    /**
     * Exact provider curvature when the selected law supplies it.
     *
     * The property is absent for custom first-order-only laws so the global
     * incremental-potential preflight can refuse incomplete provider mixtures.
     */
    readonly evaluatePotentialHessianVectorAt: ((positionOf: XpbdParticlePositionQueryN, directionOf: XpbdParticleDirectionQueryN) => SimplexConstitutiveFamilyHessianVectorEvaluationN<TMaterial, TEvaluation>) | undefined;
    /**
     * One exact additive Hessian block per source simplex when curvature exists.
     */
    readonly potentialHessianBlocks: readonly SimplexConstitutiveFamilyHessianBlockN<TMaterial>[] | undefined;
    /** Exact source-simplex block evaluation, absent for first-order-only laws. */
    readonly evaluatePotentialHessianBlockVectorAt: ((block: XpbdConservativeHessianBlockN, positionOf: XpbdParticlePositionQueryN, directionOf: XpbdParticleDirectionQueryN) => SimplexConstitutiveHessianVectorEvaluationN<TEvaluation>) | undefined;
    private readonly restPositions;
    private attachedWorld;
    private constructor();
    static compile<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>>(options: CompileSimplexConstitutiveFamilyNOptions<TMaterial, TEvaluation>): SimplexConstitutiveFamilyN<TMaterial, TEvaluation>;
    evaluate(): SimplexConstitutiveFamilyEvaluationN<TMaterial, TEvaluation>;
    /** Evaluates energy and force at a pure candidate position query. */
    evaluateAt(positionOf: XpbdParticlePositionQueryN): SimplexConstitutiveFamilyEvaluationN<TMaterial, TEvaluation>;
    private evaluateHessianVectorAt;
    private evaluateHessianBlockVectorAt;
    /** Defensive copy of the compiled material rest simplex in source-cell order. */
    restPositionsOfElement(elementIndex: number): readonly VecN[];
    /** Refuses if any retained source cell has been retired or replaced. */
    assertCurrentLineage(operation: 'evaluate' | 'evaluateAt' | 'evaluatePotentialHessianVectorAt' | 'evaluatePotentialHessianBlockVectorAt' | 'addToWorld'): void;
    /** Registers this family as a force provider; particles must already belong to the world. */
    addToWorld(world: XpbdWorldN): XpbdWorldN;
}
export declare function compileSimplexConstitutiveFamilyN<TMaterial, TEvaluation extends SimplexConstitutiveEvaluationN<TMaterial>>(options: CompileSimplexConstitutiveFamilyNOptions<TMaterial, TEvaluation>): SimplexConstitutiveFamilyN<TMaterial, TEvaluation>;
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